最后让明了块复合矩阵可对角化的一个充要条件。
Finally, a sufficient and necessary condition of the diagonalizable block compound matrices is proved.
在保持了该算法快速收敛优点的同时，利用相关矩阵块三对角的特殊结构，降低了该算法的计算复杂度。
This new method reduces the computational complexity by using the block tridiagonal structure of the input sample correlation matrix, and at the same time keeps the property of fast convergence.
讨论了一类块三对角矩阵的求逆问题。
The inverse of a class of block tridiagonal matrices is investigated.
引进了拟块有向边覆盖对角占优矩阵概念，给出了新的矩阵非奇异判定定理和特征值分布定理。
We introduced the concept of block directed edge cover diagonal quasi dominant matrix, obtained a new nonsingularity criteria for matrices and distribution theorem on eigenvalues of matrix.
证明了有限元求解的刚度矩阵是一个块对角阵，且其子矩阵是某种对称、块循环矩阵。
It is proved that the stiffness matrix of the finite element solution is a block diagonal matrix and its elements are some symmetric and block circulant submatrices.
该算法比已有的块三对角矩阵求逆算法的计算复杂度和计算时间低。
The computing complexity and computing time of this algorithm is lower than that of existed algorithms.
根据块三对角矩阵的特殊分解，给出了求解块三对角方程组的新算法。
A new algorithm of solving block tridiagonal systems is proposed, which is based on the special factorization of block tridiagonal matrix.
利用矩阵的块对角占优、广义严格对角占优以及非奇异m -矩阵的性质及理论，给出了矩阵非奇异的判定条件，拓展了矩阵非奇异性的判定准则。
Based on the properties of block diagonally dominant matrices, generalized strictly diagonally dominant matrices and nonsingular M-matrices. We give the new condition of nonsingular matrices.
由块三对角矩阵的LU分解，得到了其逆矩阵块元素的显式表达式。
With the LU decomposition of the block tridiagonal matrix, an explicit expression of the block inverse elements is obtained.
这里主要也是根据第二部分的思想，将块循环矩阵对角化，从而简化了我们的运算。
The calculations are simple to given the diagonalization of circulate matrix according the second part in the paper.
这里主要也是根据第二部分的思想，将块循环矩阵对角化，从而简化了我们的运算。
The calculations are simple to given the diagonalization of circulate matrix according the second part in the paper.
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